INVARIANT CURVES FOR AREA-PRESERVING TWIST MAPS FAR FROM INTEGRABLE

One-parameter families of area-preserving twist maps of the form F-epsilon(x, y) = (x + y + epsilon-f(x), y + epsilon-f(x)) are considered. Various invariant curves, for the maps corresponding to f(x) = sin x and f(x) = sin x + (1/50) sin(5x), are rigorously constructed for large values of the nonlinearity parameter-epsilon. For larger values of epsilon, close to critical, some numerical experiments are briefly discussed.